reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem Th19:
  Hom(a[x]b,a) <> {} & Hom(a[x]b,b) <> {}
proof
  set c = (the CatProd of C).(a,b), p1 = (the Proj1 of C).(a,b), p2 = (the
  Proj2 of C).(a,b);
  c is_a_product_wrt p1,p2 by Def8;
  then
A1: dom p1 = c & dom p2 = c;
  cod(p1) = a & cod(p2) = b by Def8;
  hence thesis by A1,CAT_1:1;
end;
